Chứng minh rằng: 1/5 +1/15 +1/25 +.......+1/1985 <9/20
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Chứng minh rằng: 1/5 + 1/15 + 1/25 +...+ 1/1985 < 0
Chứng minh rằng 1/5 + 1/15 + 1/25 + ... + 1/1985 < 9/20
Chứng minh rằng: 1/5 + 1/ 15 + 1/ 25 +......+ 1/1985 < 9/ 20
Chứng minh rằng: 1/5+1/15+1/25+...+1/1985<9/20
Chứng minh rằng: 1/5+1/15+1/25+...+1/1985<9/20
Chứng minh rằng: 1/5 + 1/15 + 1/25 +...+ 1/1985 < 9/20
Đặt \(A=\dfrac{1}{5}+\dfrac{1}{15}+\dfrac{1}{25}+...+\dfrac{1}{1985}\)
\(A=\dfrac{1}{5}.\left(1+\dfrac{1}{3}+\dfrac{1}{5}+...+\dfrac{1}{397}\right)\)
\(A=\dfrac{1}{5}.\left(1+\dfrac{1}{1+2}+\dfrac{1}{2+3}+...+\dfrac{1}{198+199}\right)\)
\(A=\dfrac{1}{5}.\left(1+1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{198}-\dfrac{1}{199}\right)\)
\(A=\dfrac{1}{5}.\left(2-\dfrac{1}{199}\right)\)
\(A=\dfrac{397}{995}< \dfrac{9}{20}\)
\(\Rightarrow\dfrac{1}{5}+\dfrac{1}{15}+\dfrac{1}{25}+...+\dfrac{1}{1985}< \dfrac{9}{20}\left(đpcm\right)\)
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Chứng minh rằng:
1/5+1/15+1/25+.....+1/1985 < 9/4
chứng minh rằng: 1/5 +1/15+1/25+...+1/1985<9/20
Chứng minh rằng: 1/5+1/15+1/25.......+1/1985<9/20